The Knowledge Base Paradigm

for

Decision Management

Decision Representation

  • Business Rules
  • Decision Tables
  • Business Processes
  • DMN
    • Decision Tables
    • FEEL
  • Logic

Declarative

Problem Solving

  • Deductive logic – deduction
  • Query languages (SQL, datalog) – query answering 
  • Constraint programming – constraint solving  
  • Logic Programming – programming
  • Abductive Logic Programming – abduction
  • Inductive Logic Programming - induction
  • PDDL, strips – planning
  • Answer set programming – model generation

Declarative

Problem Solving

Focus on a single specific form of inference

=> One representation, one problem 

Knowledge Base

Paradigm

Information

≠ Solution

≠ Problem description

= Passive, independent of specific problem

=> One representation, many problems

Knowledge Base

Paradigm

FO(.)

  • IDP's Representation Language
    • Extension of first-order logic: 
      • Types
      • Arithmetic
      • Aggregates
      • Inductive definitions
      • ...
    • Formal Model Semantics

Decision Logic

+

Decision

Specification

+

Inference

Decision Management

Knowledge Base Paradigm

Modelling Business Decisions

An Example

Car Insurance

DMN - DRD

Potential Theft Rating

  • A car's theft rating is high if any of the following applies:
    • The car is a convertible
    • The car's price is over $45 000
    • The car's model is on the High Theft Probability Auto list  
  • If all of the following are true the car's theft rating is moderate: 
    • ​The car's price is between $20 000 and $45 000
    • The car's model is not on the High Theft Probability Auto list
  • ​If all the following are true the car's theft rating if low: 
    • ​The car's price is lower than $20 000
    • The car's model is not on the High Theft Probability Auto list

Decision Table

Potential Theft Rating

Definition

Potential Theft Rating

FO(ID) Definitions

A definition ∆ of the logic FO(ID) is a set of definitional rules: ∀ x : (P(t) ← ϕ) where ϕ is a FO-formula and t a tuple of n-terms, both with free variables amongst x.

Decision Logic in FO(ID)

A decision's decision logic* in FO(ID) is a set of rules:

∀ x : (P(t) ← ϕ) where ϕ is a FO-formula and t a tuple of n-terms, both with free variables amongst x.

* for decisions representable by a decision table

Decision Table

Functionality

  • Completeness checking
  • Exclusivity checking
  • Invokation

Decision Logic Definition

Functionality

  • Completeness checking
  • Exclusivity checking
  • Compliance checking
  • Invokation

{

counter examples

Complete Input

Incomplete Input

Alternatives

Completeness*

At least one outcome for every input value assignment

 

Violated if: 

There exists a value assignment for which there is no outcome. 

Exclusiveness*

At most one outcome for every input value assignment

 

Violated if: 

There exists a value assignment for which there is more than one outcome. 

\exists \bar{X} : \neg \exists \bar{Y} : P(\bar{X}, \bar{Y})
X¯:¬Y¯:P(X¯,Y¯)\exists \bar{X} : \neg \exists \bar{Y} : P(\bar{X}, \bar{Y})

* Weak forms of completeness & exclusiveness

\exists \bar{X} : \exists_{>1} \bar{Y} : P(\bar{X}, \bar{Y})
X¯:>1Y¯:P(X¯,Y¯)\exists \bar{X} : \exists_{>1} \bar{Y} : P(\bar{X}, \bar{Y})

Stronger

Requires quantification over rules

=> rule reification

 

Compliance

Check whether the decision logic satisfies a certain property

 

"Minors can not be insured as drivers"

Violated if: 

It is possible for someone younger than 18, to be insured. 

 

 

\exists c ~ d : Covers(c, d) \wedge DriverAge(d) < 18 \wedge EligibleForInsurance(c, eligible)
c d:Covers(c,d)DriverAge(d)<18EligibleForInsurance(c,eligible)\exists c ~ d : Covers(c, d) \wedge DriverAge(d) < 18 \wedge EligibleForInsurance(c, eligible)

Invokation

  • Invoke decision with
    • all input values available
    • some input values available
  • Determine input alternaties for desired outcome

Decisions

By krr

Decisions

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